Download or read book Generalized Polynomial Programming written by Gary Edmund Blau and published by . This book was released on 1967 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Primal dual Algorithm for Constrained Generalized Polynomial Programming written by Alice M. Agogino and published by . This book was released on 1984 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Application of Generalized Polynomial Programming and the Modified Method of Multiplier in Preliminary Chemical Process Design written by Fu-chuan Thomas Lee and published by . This book was released on 1983 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Applications of Generalized Polynomial Programming to Chemical Process Problems written by Richard Lee Sleeter and published by . This book was released on 1969 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Program for Manipulating and Solving Nonlinear Generalized Polynomial Optimization Problems with Geometric Programming and Symbolic Constraint Reduction written by David C. Ketchum and published by . This book was released on 1996 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computer Algebra written by R. Albrecht and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as "symbolic and algebraic computation" or "formula manipulation". Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics, for example - are necessary. In the beginning of the use of computers for symbolic algebra it soon became apparent that the straightforward textbook methods were often very inefficient. Instead of turning to numerical approximation methods, computer algebra studies systematically the sources of the inefficiency and searches for alternative algebraic methods to improve or even replace the algorithms.
Download or read book Interior point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
Download or read book GLOBAL OPTIMIZATION OF NONCONVEX GENERALIZED POLYNOMIAL DESIGN MODELS DESIGN written by CHIHSIUNG LO and published by . This book was released on 1991 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: other hand, most deterministic algorithms are restricted to certain classes of problems. In this dissertation, a deterministic approach is investigated for a special class of problems called generalized polynomial problems which occur often in engineering applications.
Download or read book Advances in Geometric Programming written by Mordecai Avriel and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1961, C. Zener, then Director of Science at Westinghouse Corpora tion, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathe matical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from Carnegie Mellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interes tingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory.
Download or read book Nondifferentiable Optimization and Polynomial Problems written by N.Z. Shor and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.
Download or read book Interior Point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1987-01-01 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered. In this book, the authors describe the first unified theory of polynomial-time interior-point methods. Their approach provides a simple and elegant framework in which all known polynomial-time interior-point methods can be explained and analyzed; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs.
Download or read book Adaptive Learning of Polynomial Networks written by Nikolay Nikolaev and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book delivers theoretical and practical knowledge for developing algorithms that infer linear and non-linear multivariate models, providing a methodology for inductive learning of polynomial neural network models (PNN) from data. The text emphasizes an organized model identification process by which to discover models that generalize and predict well. The book further facilitates the discovery of polynomial models for time-series prediction.
Download or read book A Generalized Method of Orthogonal Polynomials written by Michel Laroche and published by . This book was released on 1985 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Moments Positive Polynomials And Their Applications written by Jean Bernard Lasserre and published by World Scientific. This book was released on 2009-10-02 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP).This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials.In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.
Download or read book Application of Generalized Geometric Programming to Optimizing Polynomials written by Robert Engel Gibson and published by . This book was released on 1969 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computing Generalized Nash Equilibria by Polynomial Programming written by Philipp Renner and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not need any convexity assumptions on either the utility functions or the action sets. The key idea is to use Putinar's Positivstellensatz, a representation result for positive polynomials, to replace each agent's problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset.
Download or read book Generalized Polynomial Optimization in an Augmented Primary Space Using General Quadratic Approximation written by Shensheng Zhang and published by . This book was released on 1987 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
